Transformations Practice Quiz: Figure A to B

Reflection is the transformation that mirrors a figure over a designated line, producing a mirror image. This flip is the most straightforward example of a reflection in geometry.

A 180-degree rotation about the center inverts a figure while preserving its size and shape. This half-turn rotation is fundamental for understanding symmetry and rotational transformations.

A translation moves every point of a figure by the same distance in the same direction while keeping the figure's orientation and size unchanged. This consistent shift is a key example of a rigid motion.

Dilation scales a figure up or down by a constant factor, thereby changing its size while preserving its shape. This transformation is crucial for understanding concepts of similarity in geometry.

Flipping a diagram involves creating a mirror image of the figure, which is achieved through reflection. This transformation is central to many spatial reasoning activities.

Reflecting a point over the y-axis changes the sign of the x-coordinate while leaving the y-coordinate unchanged. This rule is a fundamental aspect of coordinate transformations.

A 90-degree counterclockwise rotation about the origin sends (x, y) to (-y, x) based on the rotation matrix. This transformation is essential for working with rotated coordinates.

A reflection reverses the orientation of a figure, and when combined with a translation (which preserves size), the image remains congruent but with a changed orientation. This demonstrates the effect of composite rigid motions.

Translation shifts every point of a figure uniformly in a given direction without altering its size or shape. This consistent displacement is characteristic of translations.

The composition of two reflections over intersecting lines is equivalent to a rotation about the intersection point, with the angle of rotation being twice the angle between the lines. This is a key theorem in transformation geometry.

Dilation changes the size of a figure while preserving its shape, meaning the angle measures remain constant. This invariance is central to the concept of similarity in geometry.

Reflections force students to mentally construct mirror images, which challenges their ability to manipulate and understand spatial relationships. This practice enhances visual and spatial reasoning skills.

Translation moves a figure without changing its size, shape, or orientation, thus producing a congruent image in a different location. This is a classic example of a rigid motion.

Rigid motions, including translations, rotations, and reflections, preserve both distances and angle measures. This ensures that the original figure and its transformed image are congruent.

Reflection reverses the orientation of a figure, turning a clockwise arrangement into a counterclockwise one or vice versa. This reversal is a key property of reflection transformations.

Reflecting a figure and then rotating it 90 degrees clockwise about a point on the reflecting line results in a transformation equivalent to reflecting over a new line. This new line is rotated 45 degrees relative to L, which confirms the composite is a reflection.

A 270-degree counterclockwise rotation (equivalent to a 90-degree clockwise rotation) followed by a reflection over the x-axis results in swapping the x and y coordinates. This transformation is equivalent to reflecting over the line y = x.

Reflecting over two lines (one vertical and one horizontal) and incorporating a translation can combine to form a 180-degree rotation about a specific point. This composite transformation preserves distances and reorients the figure.

A dilation with a scale factor of 1 does not change the figure at all, acting as the identity transformation. Therefore, the only effect comes from the rotation, which reorients the figure without altering its size.

Reflecting over two parallel lines results in a translation, with the displacement equal to twice the distance between the lines. When followed by an additional translation upward, the net effect is a single translation whose displacement is the vector sum of the two individual translations.